Problem: Which of the following numbers is a factor of 102? ${3,5,7,9,10}$
Explanation: By definition, a factor of a number will divide evenly into that number. We can start by dividing $102$ by each of our answer choices. $102 \div 3 = 34$ $102 \div 5 = 20\text{ R }2$ $102 \div 7 = 14\text{ R }4$ $102 \div 9 = 11\text{ R }3$ $102 \div 10 = 10\text{ R }2$ The only answer choice that divides into $102$ with no remainder is $3$ $ 34$ $3$ $102$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $3$ are contained within the prime factors of $102$ $102 = 2\times3\times17 3 = 3$ Therefore the only factor of $102$ out of our choices is $3$. We can say that $102$ is divisible by $3$.